SUPPLEMENTARY to Barrie England's answer
As Barrie says, syntactically working may act as a noun or as an adjective or as a component of the progressive construction.
But the entire phrase working for the man means a bit more than this, as is suggested by Barrie's citation of John Fogerty's “Proud Mary”. Note particularly the capitalization: The Man.
Where I come from, the US South, The Man is not any particular man—he is Authority, and not benevolent Authority either. In a particular situation The Man may be your employer, he may be the overseer of your work gang, he may be the principal of your high school, he may be the owner of the land you farm as a sharecropper, he may be the sheriff of your county, and in all these capacities he has a personal name and a title; but as The Man he’s just the guy who exercises the power of the community over you, and employs it to make his life easy and your life miserable.
Unless you are yourself The Man, your lot is to spend your life Workin for the Man.
I suspect that the term arose among African-Americans, who suffered most terribly under The Man’s oppressions; but it was already current among whites, too, when I was a teenager. In 1962 Roy Orbison wrote a song that translates the old worksong style into a C&W idiom:
"Working For The Man"
Hey now you better listen to me everyone of you
We got a lotta lotta lotta lotta work to do
Forget about your woman and that water can
Today we’re working for the man
Well pick up your feet
We’ve got a deadline to meet
I’m gonna see you make it on time
I want elbows and backs
I wanna see everybody from behind
’Cause you’re working for the man working for the man
You gotta make him a hand when you're working for the man
Oh well I’m pickin’ ’em up and I’m laying ’em down
I believe he’s gonna work me into the ground
I pull to the left I heave to the right
I wanna kill him but it wouldn't be right
’Cause I’m working for the man working for the man
gotta make him a hand when you’re working for the man
Well the boss man’s daughter sneaks me water
everytime her daddy’s down the line
she says meet me tonight love a me right
and everything is gonna be fine
So I slave all day without much pay
’cause I’m just abiding my time
’cause the company and the daughter you see
They’re both gonna be all mine
Yah I’m gonna be the man gonna be the man
Gotta make him a hand if I'm gonna be the man
working for the man working for the man
gonna be the man gonna be the man
Gotta make him a hand working for the man
In the last generation or so the term has migrated out of the rural proletariat into the higher reaches of salary-slavery. There Working for The Man signifies corporate employment as opposed to “entrepreneurship”: take a look at these blog posts:
“5 reasons working for The Man isn't all that bad”
“How To Survive Working For ‘The Man’”
This is a Kinder, Gentler Man; but at bottom he’s still The Man.